Solid geometry, stereometrySolid geometry is the name for the geometry of three-dimensional Euclidean space.
Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.
- Pyramid four sides
In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
- The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
- Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
- Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
- Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
- Support colum
Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
- Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
- Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
- Roof 8
How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
- Regular triangular prism
Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- The cylinder base
The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
- Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
- Roof of the church
The cone roof of the church has a diameter of 3m and a height of 4m. What is the size of the side edge of the church roof (s) and how much sheet will be needed to cover the church roof?
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